Best-possible bounds on the set of copulas with given degree of non-exchangeability |
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| Authors: | G Beliakov B De Baets H De Meyer RB Nelsen M Úbeda-Flores |
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| Institution: | 1. School of IT, Deakin University, Burwood 3125, Australia;2. Department of Mathematical Modelling, Statistics and Bioinformatics, Ghent University, Coupure links 653, B-9000 Gent, Belgium;3. Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Krijgslaan 281 S9, B-9000 Gent, Belgium;4. Department of Mathematical Sciences, Lewis & Clark College, 0615 S.W. Palatine Hill Rd., Portland, OR 97219, USA;5. Department of Mathematics, University of Almería, Carretera de Sacramento s/n, 04120 La Cañada de San Urbano, 04120 Almería, Spain |
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| Abstract: | We establish best-possible bounds on the set of quasi-copulas with given degree of non-exchangeability. These bounds are shown to be best-possible bounds as well for the set of copulas with given degree of non-exchangeability, and, consequently, also on the set of bivariate distribution functions of continuous random variables with given margins and given degree of non-exchangeability. Non-exchangeability of a (quasi-)copula is measured in the sense of Nelsen, i.e.?proportional to the maximal absolute difference between this (quasi-)copula and its transpose. |
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| Keywords: | Best-possible bounds Copula Lipschitz condition Measure of non-exchangeability Quasi-copula |
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